Interpolation polynomial

I need a polynomial of ( x,y) based on 2D Pascal triangle to describe a column vector of Ritz approximation functions that satisfy the boundary conditions of the problem.
problem is thin plate (submitted to classical laminate theory) of width b and length l and thickness t with its X axis coinside with its length and Y axis coinside with its width. boundary conditions are :
1- for the side of Y= 0 ....... hinged support
2- for the side of Y = b ........ fixed support
3- for the side of X=0 .......... fixed support
4- for the side of X= l ........... free side
i.e
u_o (x,y,t)= {a_1 (x,y)}^T {q_1 (t)}

v_o (x,y,t)= {a_2 (x,y)}^T {q_2 (t)}

w_o (x,y,t)= {a_3 (x,y)}^T {q_3 (t)}
i need a_i(x,y) where i =1,2,3
and
u(x,y,z,t)= u_0 (x,y,t)-z (∂w_o (x,y,t))/∂x
v(x,y,z,t)= v_0 (x,y,t)-z (∂w_o (x,y,t))/∂y
w(x,y,z,t)= w_0 (x,y,t)
it has to fulfil the initial 10 modes of the shown plate in the modal analysis compared to numerical Ansys solution for the same problem